Earlier, Dilhara Fernando used the bouncy conditions to the hilt, claiming four wickets for just 18 runs, as the Mumbai Indians restricted Bangalore Royal Challengers to a modest 122 for nine.
Chasing 123 to win, Mumbai reached the target within 16 overs with Jayasuriya scoring 54 and unbeaten batsman Tendulkar at 40.
Jayasurya became the highest hitter of sixes in the League so far taking his tally to 31 including today's four towering hits over the fence. He has also hit 57 boundaries in this edition.
With this the Mumbai Indians signed off from the inaugural IPL with 14 points from as many matches. Royal Challengers, who never got going in the cash rich tournament, finished with a poor eight points in 14 matches to take the seventh spot.
The match had no significance as both the teams had been out of contention for a semi final berth as Kings XI Punjab, Rajasthan Royals, Delhi Daredevils and Chennai Super Kings have already made the grade.
Royal Challengers captain Rahul Dravid tried a new trick, introducing Anil Kumble to open the attack hoping that the ace leg spinner would use the good bounce to the host's advantage. But Jayasurya and the most accomplished Tendulkar opening the Indians' innings nothing worked for him on a cool evening.
Jayasurya went straight into overdrive and punished Kumble as the Indian Test captain gave away 16 runs in the first two overs.
Tearaway speedster Dale Steyn was the only bowler who commanded some respect from the Mumbai batsmen.
Tendulkar seemed inspired with the belligerent Sri Lankan as he too helped himself with some fine hits to the fence one and over, scoring an unbeaten 40 off 42 balls. He hit two consecutive fours craftily eluding the short square leg off Kumble in the 16th over to take Mumbai to an easy win.
Robin Uthappa who came at the fall of Jayasurya, stood out with a spectacular cover drive off Kumble and made 19 off 17 balls to take the visitors to victory without any further hick up.
Mumbai Indians raced to their first 50 off 44 balls while the second came in even quicker time, just 31 balls. With the visitors raising their 100 in the 13th over, nothing was left for the hosts to fight back.
Tendulkar and Uthappa played sensibly to take their team towards the victory.
Earlier Dilhara Fernando used the bouncy conditions, claiming four wickets for just 18 runs, while West Indian all rounder Dwayne Smith claimed three wickets for 26 to leave Bangalore innings in a disarray. Fernando was later declered man of the match.
The match was reduced to 18 overs a side as wet ground conditions delayed the start by 90 minutes.
The hosts, who have lost five out of the six home matches earlier, disappointed the good crowd again as they got themselves bogged down.
This happened once the burly Sri Lankan struck telling blows in the sixth and eighth over of the match using the conditions which was helpful to medium pacers.
West Indies' Dwayne Smith claimed three wickets for 26 to leave Bangalore in disarray.
Tail enders Vinay Kumar (23) and Praveen Kumar (8) added 39 runs for the eighth wicket in just 25 balls to give some respectability to the Bangalore innings.
The two joined together with Royal Challengers struggling at 83 for seven and took the score to 122 before Vinay was holed out to Uthappa at the long-on fence giving Fernando his fourth wicket.
Royal Challengers began well with the teenage opener Sreevats Goswamy (20) and South African stumper batsman Mark Boucher (18) giving a purposeful start adding 35 runs in less than six overs.
But once Fernando came to bowl replacing Nehra, he put skids to Bangalore innings dismissing Boucher and Misbah in his first over and sent Goswamy back to pavilion in his second over.
This put the home team in the same position that they found themselves in many times earlier in this league.
They lost too many wickets too early. The run rate slowed down and they never recovered.
Misbah was dismissed for a duck disappointed again, while Dravid again got out, castled by Smith, after he left his wickets wide open to guide the ball to the third man.
The disappointing stint of Under-19 World Cup winning captain Virat Kohli continued as he, too, was dismissed for a duck played clumsily to a lifting delivery from Nehra.
Mumbai Indian's skipper Sachin rotated his bowlers well despite young medium pacer Dhawal Kulkarni disappointing him with wayward bowling conceding 34 runs in his three overs.